Modern Physics as Classical Physics 1

Let's now fill in details to the items 1-4 of this post. We start with 1 expressing a main stumbling block for classical physics as instant action at distance asking for an infinite speed of propagation of gravitational force. This is how the Universe apparently is designed: If there was a delay by finite speed of propagation of gravitational force, the Earth would spin out from its elliptic track around the Sun, a fact acknowledged by everybody including modern physicists. Newton accepted apparent infinite speed of gravitational force as a necessary fact to make the Universe turn around as observed.  

Then came Einstein with his General Theory of Gravitation GR as modern physics with the speed of gravitation equal to the speed of light. In oder to make GR fit with observation somehow the delay from finite speed of gravitation had to compensated by some other effect of GR exactly cancelling the delay, and it was claimed that GR upon difficult close inspection in fact contained such a forbet prediction effect although impossible to verify, since the equations of GR are impossible to solve in any generality. 

The problem of apparent infinite speed of gravitation thus remained in modern physics as a true mystery. Einstein’s brilliant idea that the speed of gravity is equal to the speed of light in vacuum lacks physical explanation. The speed of light through glass is smaller than in a vacuum. Is it the same for gravity? Probably not since gravitation shielding is impossible, while pulling the curtain keeps light out.

But there is a way of looking at Newtonian gravitation, where instant action at distance is replaced by local instant action, where the infinite speed of gravitation is only an apparent non-real effect. The argument is this: Newtonian gravitation is described by Poisson's equation 

• $\rho (x,t)=\Delta\phi (x,t)$,         (N)

where $\rho (x,t)$ is mass density at the point $x$ in Euclidean space and time $t$, $\phi (x,t)$ is gravitational potential and $\Delta$ is the Laplace differential operator acting on $x$ as a local operation of differentiation. 

The standard way of looking at the equation (N) creating problems, is to think of mass density $\rho$ as given and gravitational potential $\phi$ as a derived quantity obtained by solving Poisson's equation $\Delta\phi =\rho$, which is a global process asking for infinite speed of gravitation.

But there is another way, and that is to view $\phi$ as given and $\rho =\Delta\phi$ as a derived quantity obtained by the local operation of differentiation, which does not require infinite speed of gravity. This means that the gravitational potential is giving mass to matter as an instant local operation compatible with a finite speed of gravitation, to be compared with the standard view that mass creates gravitational potential as an instant global operation asking for infinite speed of gravitation.  

In the new view mass conservation takes the form 

• $\frac{\partial}{\partial t}\Delta\phi +\nabla\cdot m=0$,

where $m$ is momentum, which can be seen as recipe for updating $\phi$ from $m$ without need of infinite speed of gravitation. We could view the recipe being effected computationally with the speed of gravitation tending to infinity, without the computation representing physics.

We can also view (N) as gravitational potential and mass density acting in lock-step, as a form of perfect harmony in the sense of Leibniz.

In this perspective, where gravitational potential gives mass to matter by local instant differentiation, there is no need of any gravitons as some form of gravitational force-carrying fundamental particles. This could be seen as a great relief to an open-minded modern physicist, since no gravitons have been found. 

This is described in more detail in these posts.

The reason why to human beings matter has been viewed primordial with gravitational potential somehow generated by presence of mass, asking for infinite speed of gravitational force, is probably that to humans presence of matter can be seen (the Sun), while gravitational potential cannot be seen, only felt as  gravitational force as gradient of gravitational potential. To a blind person for whom only the feel of gravitational force is present, the new view may be more natural. 

Has the new view been inspected and discarded as crank physics by modern physicists speaking about gravitons without observations?